Retirement Number Calculator

Using scientific principles this calculator computes the age at which
your pre-retirment contributions should be sufficient to meet your
retirement needs. And it explains how the results were derived.

This calculator does not include a questionnaire on risk tolerance
(your psychological ability to stomach investment losses). Instead it
primarily concerned with computing the appropriate strategy given your risk
aversion (preference for uniform consumption).

Several things set this calculator apart:

A balance sheet approach - asset allocation can't be performed in
isolation, but must be performed by taking into account the presence
and size of Social Security, Pensions, 401(k)'s, income annuities, and
home equity. See the FAQ for more
details.

Future contributions - the impact of any possible future
contributions is handled by entering their expected annual amount,
growth rate, and volatility.

A true risk free asset - liability matching bonds, that is
inflation indexed zero coupon bonds with a duration matching that of
anticipated retirement cash flows, not cash, are used as the true risk
free asset. Liability matching bonds might be hard to purchase, but a
TIPS ladder, or a TIPS bond fund of appropriate duration, is a close
substitute.

Income annuities - income annuities are a valuable tool in the
retirement toolbox. This calculator optionally recommends the
purchase of inflation indexed income annuities, be they single premium
immediate annuities or deferred income annuities.

Home equity - home equity is the largest asset class for many
individuals. It is thus important to consider the appropriate role of
home equity in the retirement planning process.

Admit what we don't know - returns from the stock market are
intrinsically unknown. We generate a range of results for different
plausible scenarios.

Cross validated - sample Merton's method recommendations produced
by this calculator have been
cross validated with a
second asset allocator that uses stochastic dynamic programming.

Longevity

Enter your total life expectancy if known, or leave blank to have your
life expectancy computed using U.S. Social Security Administration
data.

Financial position

This section highlights the balance sheet nature of the approach used. Any asset can essentially be thought of as a series of future cash flows that may be certain or uncertain to some degree. This is true not only of the future cash flows from stocks and bonds, but also such items as future Social Security or pension payments as well as future contributions to retirement savings.

Existing defined benefits:

Owner self/spouse

Starting age

Annual amount

Inflation indexed

Death benefit Contingent/survivor payout

Social Security

%

Social Security

%

%

%

%

%

%

%

%

%

%

Reverse mortgage is for a reverse mortgage providing a fixed annual income (tenure) only.
Starting age is that of the owner. Annual amount is in current inflation-adjusted
after tax dollars, not future dollars. For income annuities, which become fully
taxable after a certain age, enter the expected average after tax amount.
Payouts last at least as long as the owner's life.
Contingent: payout reduced on death of either party.
Survivor: payout reduced only on death of the owner.

Variable annuities are not recommended as an investment
vehicle, but during the accumulation phase principal spent purchasing
variable annuities should be handled similarly to after tax investments
and earnings on variable annuities should be handled similarly to
pre-tax investments. During the payout phase variable annuities are
best listed, albeit imprecisely, under defined benefits.

Contributions and mortgage payments (below) are combined on the
assumption that once the mortgage is paid off the additional funds
will go towards retirement savings. Contribution amount should consist
only of new money contributed to your retirement savings, not the
payout from any existing pre-retirement defined benefits. Reduction
when only one spouse is working will normally equal the after tax
income of the retired spouse, should be expressed prior to applying
any growth rate, and can exceed the contribution amount if drawdown is
then occuring. A growth
rate of 5% represents a doubling every 14 years.
Remember to take into account life events such as promotions, or
children leaving home in estimating the growth rate.

Mortgage balance should include the mortgage balance of any existing
reverse mortgage, in which case the annual payment will normally be
zero and the APR value used is irrelevant.

Financial goals

Age of spouse at their retirement (blank to retire at the same time as you):
Relative income required when one party deceased: %
Annual desired retirement consumption level:

Retirement consumption should be expressed in current
inflation-indexed dollars.

Use liability matching bonds :

Inflation-indexed liability matching bonds are a valuable retirement
planning tool. However the short term volatility of long duration
liability matching bonds may make them unattractive to investors with
a low risk tolerance. If liability matching bonds are not used we
naively replace them with regular bonds.

Permit recommendation of income annuities :

Income annuities only make sense if you are in reasonable health and
are not planning on leaving an estate.

Permit recommendation of a variable rate reverse mortgage:

Reverse mortgages only make sense if you are not planning on leaving
an estate. Many retirees use home equity as a last resort to pay for
long term care. If you elect to consider a reverse mortgage you should
make sure you either have long term care insurance, or that you still
have sufficient assets to pay for your long term care needs.

For a HECM reverse mortgage the index interest rate should be the 10-year
constant maturity Treasury or 10-year LIBOR swap rate. This is true
even though you will have a monthly or annually adjusting reverse
mortgage.

We do not support the ability to leave a specific bequest amount.

Market parameters

You can probably leave the parameters in this section alone.

Estimated equity arithmetic real return: %
Volatility: %

U.S. market average values for 1927-2016 are 8.7% and 19.4%.
World market average values for 1900-2000 are 7.2% and 17.0%.
Going
forward many
experts predict lower U.S. stock market returns.

Estimated premium of an average bond portfolio over 10 year constant
maturity Treasuries is 0.6%. Estimated U.S. bond market average real
volatility for 1927-2016 was 8.7%. Survey of Professional Forecasters
2017Q1 10 year inflation rate was 2.3%.

Using the default parameters no regular bonds may be recommended. This
will occur if regular bonds have a lower expected return than zero
long-term volatility inflation indexed liability matching bonds.

Synthetic historical values for 1972-2016 for coupon bonds are 4.8%
and 23.9%. Zero coupon bonds will be similar.

Standard error of estimate of equity real return : %

U.S. market average value for 1927-2016 is 2.0%.
World market average value for 1900-2000 is 1.7%.

Also report results forming a %
confidence interval for the equity return.

Equity and regular bond management fee: %

A value around 0.1% is typical for a low cost provider such
as Vanguard.

Real interest rate: %
Yield curve date:

Fixed interest rates can be specified, or if left blank the Treasury
yield curves for the specified date will be used. When a fixed real
rate is used a fixed nominal rate is formed by combing the fixed real
rate, the projected inflation rate, and the regular bonds premium.

Well being

Coefficient of relative risk aversion, γ:

This determines how risk averse you are. A value such as 1 represents
a low degree of risk aversion and favors stocks. A value such as 5
represents a high degree of risk aversion and favors bonds. Risk
aversion is not the same as risk tolerance. Risk tolerance is about
how psychologically comfortable you are with losses to your investment
assets. Risk aversion is about how you feel about a change in your
annual consumption.
Economists are
divided on an appropriate value for γ. Many think it is in
the range 1 to 4. Others consider a value
of 10 or even higher reasonable. Marginal utility of consumption,
U'(C) = C-γ.

This is a difficult concept. We present multiple tables to help you
get this important parameter right.

As γ increases the desirability of risk taking decreases.

γ

1

2

3

4

5

Indifference to a 50/50 chance of consuming either 100% of C or 200%
of C versus consuming the guaranteed fixed percentage of C shown

141%

133%

126%

121%

117%

The value of an additional dollar declines as you consume more.

γ

1

2

3

4

5

Value of an additional dollar when consuming 110% of C compared
to the value of an additional dollar when consuming 100% of C

91%

83%

75%

68%

62%

The value of an additional dollar declines rapidly for high consumption levels.

γ

1

2

3

4

5

Value of an additional dollar when consuming 200% of C compared
to the value of an additional dollar when consuming 100% of C

Risk tolerance is concerned with the ability to psychologically handle
losses to your investment portfolio, and not pull out of the market in
the event of a downturn. Risk tolerance differs from risk aversion by
only looking at investment assets rather than the total portfolio
including defined benefits. Setting it to a low or intermediate value
provides for peace of mind but will reduce your expected
consumption. In an ideal world it might be set as high as possible so
that risk aversion, which looks at the total portfolio, can take over
in determining the appropriate asset allocation. For the default
market parameters a value of 18% or higher effectively imposes no
constraints. Setting it to a value of 10% or less is only possible for
ages above about 40, or if you also alter the default market
parameters to be indicative of shorter-term bonds.